Valuing Employee Stock Options Part 3 pptx

CHAPTER
3
Impact on Valuation
A BRIEF DESCRIPTION OF
THE DIFFERENT METHODOLOGIES
In options analysis, there are three mainstream methodologies and ap-
proaches used to calculate an option’s value:
1. Closed-form models like the Black-Scholes model (also known as the
Black-Scholes-Merton model, henceforth known as BSM) and its mod-
ifications such as the Generalized Black-Scholes model (GBM)
2. Monte Carlo path-dependent simulation methods
3. Lattices (binomial, trinomial, quadranomial, and multinomial lattices)
However, the mainstream methods that are most widely used are the closed-
form models (BSM and GSM) and the binomial lattices. No matter which
types of stock options problems you are trying to solve, if the binomial lattice
approach is used, the solution can be obtained in one of two ways. The first
is the use of risk-neutral probabilities, and the second is the use of market-
replicating portfolios. Throughout the analysis, the risk-neutral binomial lat-
tice approach is used—and can be simply termed “binomial lattices.”
1
The
use of a replicating portfolio is more difficult to understand and apply, but
the results obtained from replicating portfolios are identical to those ob-
tained through risk-neutral probabilities. So it does not matter which method
is used; nevertheless, application and expositional ease should be empha-
sized, and thus the risk-neutral probability method is preferred.
SELECTION AND JUSTIFICATION
OF THE PREFERRED METHOD
Based on the analysis in Chapter 5 and my prior published study that
was presented to the FASB’s Board of Directors in 2003, it is concluded
19

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that the BSM, albeit theoretically correct and elegant, is insufficient and
inappropriately applied when it comes to quantifying the fair-market
value of ESOs.
2
This is because the BSM is applicable only to European
options without dividends, where the holder of the option can exercise
the option only on its maturity date and the underlying stock does not
pay any dividends.
3
However, most ESOs are American-type
4
options with dividends,
where the option holder can execute the option at any time up to and in-
cluding the maturity date while the underlying stock pays dividends. In ad-
dition, under real-world conditions, ESOs have a time to vesting before the
employee can execute the option, which may also be contingent upon the
firm and/or the individual employee attaining a specific performance level
(e.g., profitability, growth rate, or stock price hitting a minimum barrier
before the options become live), and are subject to forfeitures when the
employee leaves the firm or is terminated prematurely before reaching the
vested period. In addition, certain options follow a tranching or graduated
scale, where a certain percentage of the stock option grants become exer-
cisable every year.
5
Next, the option value may be sensitive to the expected
economic environment, as characterized by the term structure of interest
rates (i.e., the U.S. Treasuries yield curve) where the risk-free rate can
change during the life of the option. Finally, the firm may undergo some
corporate restructuring (e.g., divestitures, multinational operations, or

mergers and acquisitions that may require a stock swap that changes the
volatility of the underlying stock). All these real-life scenarios make the
BSM insufficient and inappropriate when used to place a fair-market value
on the option grant. In summary, firms can implement a variety of provi-
sions that affect the fair value of the options; the above list is only a few
examples. The closed-form models such as the BSM or the GBM—the lat-
ter accounts for the inclusion of dividend yields—are inflexible and cannot
be modified to accommodate these real-life conditions. Hence, the bino-
mial lattice approach is chosen.
It is shown in Chapter 5 that under very specific conditions (European
options without dividends), the binomial lattice and Monte Carlo simula-
tion approaches yield identical values to the BSM, indicating that the two
former approaches are robust and exact at the limit. However, when spe-
cific real-life business conditions are modeled (i.e., probability of forfeiture,
probability that the firm or stock underperforms, time-vesting, suboptimal
exercise behavior, and so forth), only the binomial lattice with its highly
flexible nature will provide the true fair-market value of the ESO. Binomial
lattices can account for real-life conditions such as stock price barriers (a
barrier option exists when the stock option becomes either in-the-money
20 IMPACTS OF THE NEW FAS 123 METHODOLOGY
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or out-of-the-money only when it hits a stock price barrier), vesting
tranches (a specific percent of the options granted becomes vested or exer-
cisable each year), changing volatilities (business conditions changing or
corporate restructuring), and so forth—the same conditions where a BSM
fails miserably.
The BSM takes into account only the following inputs: stock price,
strike price, time to maturity, a single risk-free rate, and a single volatility.
The GBM accounts for the same inputs as well as a single dividend rate.
Hence, in accordance with the proposed FAS 123 requirements, the BSM

and GBM fail to account for real-life conditions. On the contrary, the bino-
mial lattice can be customized to include the stock price, strike price, time
to maturity, a single risk-free rate and/or multiple risk-free rates changing
over time, a single volatility and/or multiple volatilities changing over time,
a single dividend rate and/or multiple dividend rates changing over time,
plus all the other real-life factors including but not limited to vesting peri-
ods, changing suboptimal early exercise behaviors, multiple blackout peri-
ods, and changing forfeiture rates over time. It is important to note that the
customized binomial lattice results revert to the GBM if these real-life con-
ditions are negligible.
Therefore, based on the justifications above, and in accordance with
the requirements and recommendations set forth by the proposed FAS 123,
which prefers the binomial lattice, it is hereby concluded that the cus-
tomized binomial lattice is the best and preferred methodology to calculate
the fair-market value of ESOs.
APPLICATION OF THE PREFERRED METHOD
It must be noted here that a standard binomial lattice takes only the six
GBM inputs plus a step size input, and is insufficient and inadequate to
model ESOs under FAS 123. A special customized binomial lattice was de-
veloped to incorporate these additional exotic and changing inputs over
time. This customized binomial lattice is used throughout the book. Please
contact the author for further information about the software and algo-
rithms used.
In applying the customized binomial lattice methodology, several in-
puts have to be determined, including:
■ Stock price at grant date
■ Strike price of the option grant
■ Time to maturity of the option
Impact on Valuation 21
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■ Risk-free rate over the life of the option
■ Dividend yield of the option’s underlying stock over the life of the op-
tion
■ Volatility over the life of the option
■ Vesting period of the option grant
■ Suboptimal exercise behavior multiple of employees over the life of the
option
■ Forfeiture and employee turnover rates over the life of the option
■ Blackout dates when the options cannot be exercised, from the
postvesting period until maturity
The analysis assumes that the employee cannot exercise the option when it
is still in the vesting period. Further, if the employee is terminated or de-
cides to leave voluntarily during this vesting period, the option grant will
be forfeited and presumed worthless. In contrast, after the options have
been vested, employees tend to exhibit erratic exercise behavior where an
option will be exercised only if it breaches some multiple of the contractual
strike price, and not before. This is termed the suboptimal exercise behav-
ior multiple.
6
However, the options that have vested must be exercised
within a short period if the employee leaves voluntarily or is terminated,
regardless of the suboptimal behavior threshold—that is, if forfeiture oc-
curs (measured by the historical option forfeiture rates as well as employee
turnover rates). Finally, if the option expiration date has been reached, the
option will be exercised if it is in-the-money, and expire worthless if it is at-
the-money or out-of-the-money. The next section details the results ob-
tained from such an analysis. Further, Chapters 9 and 10 provide more
details on the selection and justification of the input parameters used, while
the following section provides a theoretical and empirical justification of
the results.

TECHNICAL JUSTIFICATION
OF METHODOLOGY EMPLOYED
This section illustrates some of the technical justifications that make up the
price differential between the GBM and the customized binomial lattice
models. Figure 3.1 shows a tornado chart and how each input variable in a
customized binomial lattice drives the value of the option.
7
Based on the
chart, it is clear that volatility is not the single key variable that drives op-
tion value.
8
In fact, when vesting, forfeiture, and suboptimal early exercise
behavior elements are added to the model, their effects dominate that of
volatility. Of course the tornado chart will not always look like Figure 3.1,
22 IMPACTS OF THE NEW FAS 123 METHODOLOGY
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as it will change depending on the inputs. The chart only illustrates a spe-
cific case and should not be generalized across all cases.
In contrast, volatility is a significant variable in a simple BSM as can be
seen in Figure 3.2. This is because there is less interaction among input
variables, due to the fewer input variables, and for most ESOs that are is-
sued at-the-money, volatility plays an important part when there are no
other dominant inputs.
In addition, the interactions between these new input variables are
nonlinear. Figure 3.3 shows a spider chart
9
and it can be seen that vesting,
forfeiture rates, and suboptimal behavior multiples have nonlinear effects
on option value. That is, the lines in the spider chart are not straight but
curve at certain areas, indicating that there are nonlinear effects in the

model. This means that we cannot generalize these three variables’ effects
on option value (for instance, we cannot generalize that if a 1 percent in-
crease in forfeiture rate will decrease option value by 2.35 percent, it
means that a 2 percent increase in forfeiture rate drives option value down
4.70 percent, and so forth). This is because the variables interact differ-
ently at different input levels. The conclusion is that we really cannot say a
priori what the direct effects are of changing one variable on the magni-
Impact on Valuation 23
FIGURE 3.1 Tornado chart listing the critical input factors of a customized
binomial model.
Critical Input Factors of the Custom Binomial Model
9.8
46
2%
19
91%
9%
2.9
24.5
45%
9.10
8.2
54
9%
91
53%
1%
18.1
180.5
5%

1.90
–$5.00 $5.00 $15.00 $25.00
$35.00
Vesting
Forfeiture
Stock Price
Behavior
Dividend
Volatility
Strike Price
Risk-Free Rate
Steps
Maturity
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24 IMPACTS OF THE NEW FAS 123 METHODOLOGY
FIGURE 3.2 Tornado chart listing the critical input factors of the BSM.
Black-Scholes Critical Input Factors
8.2
2%
19
15%
24.5
9.8
9%
91
91%
180.5
$(50.00) $- $50.00
$100.00 $150.00
$200.00

Volatility
Rish-Free Rate
Maturity
Stock Price
Strike Price
FIGURE 3.3 Spider chart showing the nonlinear effects of input factors in the
binomial model.
Nonlinear Critical Input Factors
$-
$10.0000
$20.0000
$30.0000
$40.0000
Percentiles of the Variables
Vesting
Forfeiture
Stock Price
Behavior
Dividend
Volatility
Strike Price
Risk-Free Rate
Steps
Maturity
10.0% 30.0% 50.0%
70.0%
90.0%
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tude of the final option value. More detailed analysis will have to be per-
formed in each case.

Although the tornado and spider charts illustrate the impact of each
input variable on the final option value, its effects are static. That is, one
variable is tweaked at a time to determine its ramifications on the option
value. However, as shown, the effects are sometimes nonlinear, which
means we need to change all variables simultaneously to account for their
interactions. Figure 3.4 shows a Monte Carlo simulated dynamic sensitiv-
ity chart where forfeiture, vesting, and suboptimal exercise behavior multi-
ples are determined to be important variables, while volatility is again
relegated to a less important role. The dynamic sensitivity chart perturbs
all input variables simultaneously for thousands of trials, and captures the
effects on the option value. This approach is valuable in capturing the net
interaction effects among variables at different input levels.
From this preliminary sensitivity analysis, we conclude that incorpo-
rating forfeiture rates, vesting, and suboptimal early exercise behavior is
vital to obtaining a fair-market valuation of ESOs due to their significant
contributions to option value. In addition, we cannot generalize each in-
put’s potential nonlinear effects on the final option value. Detailed analysis
has to be performed to obtain the option’s value every time.
Impact on Valuation 25
FIGURE 3.4 Dynamic sensitivity with simultaneously changing input factors in
the binomial model.
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OPTIONS WITH VESTING AND SUBOPTIMAL BEHAVIOR
Employee stock option holders tend to execute their options suboptimally
because of liquidity needs (pay off debt, down payment on a home, vaca-
tions), personal preferences (risk-averse perception that the stock price will
go down in the future), or lack of knowledge (firms do not provide guid-
ance to their employees on optimal timing or optimal thresholds to exer-
cise their options). Therefore, further investigation into the elements of
suboptimal exercise behavior and vesting is needed, and the analysis yields

the chart shown in Figure 3.5.
10
Here we see that at lower suboptimal be-
havior multiples (within the range of 1 to 6), the stock option value can be
significantly lower than that predicted by the BSM. With a 10-year vesting
stock option, the results are identical regardless of the suboptimal behavior
multiple—its flat line bears the same value as the BSM result. This is be-
cause for a 10-year vesting of a 10-year maturity option, the option reverts
to a perfect European option, where it can be exercised only at expiration.
The BSM provides the correct result in this case.
However, when suboptimal exercise behavior multiple is low, the op-
tion value decreases. This is because employees holding the option will
tend to exercise the option suboptimally—that is, the option will be exer-
cised earlier and at a lower stock price than optimal. Hence, the option’s
26 IMPACTS OF THE NEW FAS 123 METHODOLOGY
FIGURE 3.5 Impact of suboptimal exercise behavior and vesting on option value
in the binomial model.
Impact of Suboptimal Behavior and Vesting on Option Value
Suboptimal Behavior Multiple
Option Value
$6.00
$8.00
$10.00
$12.00
$14.00
$16.00
$18.00
Vesting (1 Year)
Vesting (2 Years)
Vesting (3 Years)

Vesting (4 Years)
Vesting (5 Years)
Vesting (6 Years)
Vesting (7 Years)
Vesting (8 Years)
Vesting (9 Years)
Vesting (10 Years)
Black-Scholes
Value
12345678 9 12131415161718192010 11
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upside value is not maximized. As an example, suppose an option’s strike
price is $10 while the underlying stock is highly volatile. If an employee
exercises the option at $11 (this means a 1.10 suboptimal exercise multi-
ple), he or she may not be capturing the entire upside potential of the op-
tion as the stock price can go up significantly higher than $11 depending
on the underlying volatility. Compare this to another employee who exer-
cises the option when the stock price is $20 (suboptimal exercise multiple
of 2.0) versus one who does so at a much higher stock price. Thus, lower
suboptimal exercise behavior means a lower fair-market value of the
stock option.
This suboptimal exercise behavior has a higher impact when stock
prices at grant date are forecast to be high. Figure 3.6 shows that (at the
lower end of the suboptimal exercise behavior multiples) a steeper slope
occurs the higher the initial stock price at grant date.
11
Figure 3.7 shows that for higher volatility stocks, the suboptimal re-
gion is larger and the impact to option value is greater, but the effect is
gradual.
12

For instance, for the 100 percent volatility stock (Figure 3.7), the
suboptimal region extends from a suboptimal exercise behavior multiple of
1.0 to approximately 9.0 versus from 1.0 to 2.0 for the 10 percent volatil-
ity stock. In addition, the vertical distance of the 100 percent volatility
stock extends from $12 to $22 with a $10 range, as compared to $2 to $10
with an $8 range. Therefore, the higher the stock price at grant date and
Impact on Valuation 27
FIGURE 3.6 Impact of suboptimal exercise behavior and stock price on option
value in the binomial model.
Impact of Suboptimal Behavior on Option Value with different Stock Prices
Suboptimal Behavior Multiple
Option Value
$0.00
$10.00
$20.00
$30.00
$40.00
$50.00
$60.00
$70.00
$80.00
Stock Price $5
Stock Price $10
Stock Price $15
Stock Price $20
Stock Price $25
Stock Price $30
Stock Price $35
Stock Price $40
Stock Price $45

Stock Price $50
Stock Price $55
Stock Price $60
Stock Price $65
Stock Price $70
Stock Price $75
Stock Price $80
Stock Price $85
Stock Price $90
Stock Price $95
Stock Price $100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18
19
20
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the higher the volatility, the greater the impact of suboptimal behavior will
be on the option value. In all cases, the BSM results are the horizontal lines
in the charts (Figures 3.6 and 3.7). That is, the BSM will always generate
the maximum option value assuming optimal exercise behavior, and over-
expense the option significantly.
OPTIONS WITH FORFEITURE RATES
Figure 3.8 illustrates the reduction in option value when the forfeiture rate
increases.
13
The rate of reduction changes depending on the vesting pe-
riod. The longer the vesting period, the more significant the impact of for-
feitures will be. This illustrates once again the nonlinear interacting
relationship between vesting and forfeitures (that is, the lines in Figure 3.8
are curved and nonlinear). This is intuitive because the longer the vesting

period, the lower the compounded probability that an employee will still
be employed in the firm and the higher the chances of forfeiture, reducing
the expected value of the option. Again, we see that the BSM result is the
highest possible value assuming a 10-year vesting in a 10-year maturity
option with zero forfeiture. The BSM will always generate the maximum
option value assuming all options will fully vest, and overexpense the op-
tion significantly.
28 IMPACTS OF THE NEW FAS 123 METHODOLOGY
FIGURE 3.7 Impact of suboptimal exercise behavior and volatility on option
value in the binomial model.
Impact of Suboptimal Behavior on Option Value with Different Volatilities
Suboptimal Behavior Multiple
Option Value
$0.00
$5.00
$10.00
$15.00
$20.00
$25.00
Volatility 10%
Volatility 20%
Volatility 30%
Volatility 40%
Volatility 50%
Volatility 60%
Volatility 70%
Volatility 80%
Volatility 90%
Volatility 100%
1 2 3 4 5 6 7 8 9 10 11121314151617181920

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OPTIONS WHERE RISK-FREE
RATE CHANGES OVER TIME
Another input assumption is the risk-free rate. Tables 3.1 and 3.2 illustrate
the effects of changing risk-free rates over time on option valuation. Due to
the time-value-of-money, discounting more heavily in the future will re-
duce the option’s value. Tables 3.1 and 3.2 compare several risk-free yield
curve characteristics: flat, upward sloping, downward sloping, smile, and
frown. Table 3.1 indicates that a changing risk-free rate over time has a
negligible effect on option value for a simple option (i.e., setting subopti-
mal exercise behavior multiple to 100, vesting to zero, forfeiture to zero,
and dividends to zero recreates a basic call option where the BSM is suffi-
cient). The changing risk-free rate in the binomial lattice yields $64.89
with 1,000 lattice steps, identical to the BSM results. Notice that the valua-
tions are identical regardless of how the risk-free rates change over time.
However, when exotic variables are included as in Table 3.2, where sub-
optimal exercise behavior multiple is 1.8, vesting is 4 years, and forfeiture
rate is 10 percent, these tend to interact with the changing risk-free rates. In
all cases, the binomial lattice taking into account the changing risk-free rate
will yield lower values than the naïve BSM and forfeiture-rate-modified
BSM results. In addition, comparing the base case scenario of a flat yield
curve or constant 5.50 percent risk-free rate (option value $25.92) with the
other scenarios, the results are now different due to this new interaction. For
instance, when the term structure of interest rates increases over time, the
Impact on Valuation 29
FIGURE 3.8 Impact of forfeiture rates and vesting on option value in the
binomial model.
Impact of Forfeitures and Vesting on Option Value
$0.00
$2.00

$4.00
$6.00
$8.00
$10.00
$12.00
$14.00
$16.00
$18.00
0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%
Probability of Forfeiture
Option Value
Vesting (1 Year)
Vesting (2 Years)
Vesting (3 Years)
Vesting (4 Years)
Vesting (5 Years)
Vesting (6 Years)
Vesting (7 Years)
Vesting (8 Years)
Vesting (9 Years)
Vesting (10 Years)
Black-Scholes value
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TABLE 3.1 Effects of Changing Risk-Free Rates on Option Value
Static Increasing Decreasing Risk-Free Risk-Free
Base Risk-Free Risk-Free Rate Rate
Basic Input Parameters Year Case Rates Rates Smile Frown
Stock Price $100.00 1 5.50% 1.00% 10.00% 8.00% 3.50%
Strike Price $100.00 2 5.50% 2.00% 9.00% 7.00% 4.00%
Maturity 10.00 3 5.50% 3.00% 8.00% 5.00% 5.00%

Volatility 45.00% 4 5.50% 4.00% 7.00% 4.00% 7.00%
Dividend Rate 0.00% 5 5.50% 5.00% 6.00% 3.50% 8.00%
Lattice Steps 1,000 6 5.50% 6.00% 5.00% 3.50% 8.00%
Suboptimal Behavior 100.00 7 5.50% 7.00% 4.00% 4.00% 7.00%
Vesting Period 0.00 8 5.50% 8.00% 3.00% 5.00% 5.00%
Forfeiture Rate 0.00% 9 5.50% 9.00% 2.00% 7.00% 4.00%
10 5.50% 10.00% 1.00% 8.00% 3.50%
Average 5.50% 5.50% 5.50% 5.50% 5.50%
BSM using 5.50% $64.89 $64.89 $64.89 $64.89 $64.89
Average Rate
Forfeiture Modified $64.89 $64.89 $64.89 $64.89 $64.89
BSM using 5.50%
Average Rate
Changing Risk-Free $64.89 $64.89 $64.89 $64.89 $64.89
Binomial Lattice
30
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TABLE 3.2 Effects of Changing Risk-Free Rates with Exotic Inputs on Option Value
Static Increasing Decreasing Risk-Free Risk-Free
Base Risk-Free Risk-Free Rate Rate
Basic Input Parameters Year Case Rates Rates Smile Frown
Stock Price $100.00 1 5.50% 1.00% 10.00% 8.00% 3.50%
Strike Price $100.00 2 5.50% 2.00% 9.00% 7.00% 4.00%
Maturity 10.00 3 5.50% 3.00% 8.00% 5.00% 5.00%
Volatility 45.00% 4 5.50% 4.00% 7.00% 4.00% 7.00%
Dividend Rate 4.00% 5 5.50% 5.00% 6.00% 3.50% 8.00%
Lattice Steps 1,000 6 5.50% 6.00% 5.00% 3.50% 8.00%
Suboptimal Behavior 1.80 7 5.50% 7.00% 4.00% 4.00% 7.00%
Vesting Period 4.00 8 5.50% 8.00% 3.00% 5.00% 5.00%
Forfeiture Rate 10.00% 9 5.50% 9.00% 2.00% 7.00% 4.00%

10 5.50% 10.00% 1.00% 8.00% 3.50%
Average 5.50% 5.50% 5.50% 5.50% 5.50%
BSM using 5.50% $37.45 $37.45 $37.45 $37.45 $37.45
Average Rate
Forfeiture Modified $33.71 $33.71 $33.71 $33.71 $33.71
BSM using 5.50%
Average Rate
Changing Risk-Free $25.92 $24.31 $27.59 $26.04 $25.76
Binomial Lattice
31
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option value calculated using a customized changing risk-free rate binomial
lattice is lower ($24.31) than that calculated using a constant or average
rate. The reverse is true for a downward-sloping yield curve. In addition,
Table 3.2 shows a risk-free yield curve frown (low rates followed by high
rates followed by low rates) and a risk-free yield curve smile (high rates fol-
lowed by low rates followed by high rates). In summary, the results indicate
that using a single average risk-free rate will overestimate an upward-
sloping yield curve, underestimate a downward-sloping yield curve, over-
estimate a yield curve frown, and underestimate a yield curve smile. The
illustration here is for a typical case and may not be generalized to include
all cases.
OPTIONS WHERE
VOLATILITY CHANGES OVER TIME
Similar to the changing risk-free rate analysis, Table 3.3 illustrates the
effects of changing volatilities on an ESO. If volatility changes over time,
the option model using a single average volatility over time will overesti-
mate the true option value of a volatility stream that gradually increases
over time starting from a low level. In all other cases, the average
volatility model will underestimate the true value of the option. The il-

lustration here is for a typical case and may not be generalized to include
all cases.
OPTIONS WHERE DIVIDEND
YIELD CHANGES OVER TIME
Dividend yield is an interesting variable that has very little interaction
with other exotic input variables. Dividend yield has a close-to-linear ef-
fect on option value, whereas the other exotic input variables do not. For
instance, Table 3.4 illustrates the effects of different maturities (in years)
on the same option.
14
The higher the maturity, the higher the option value
but the option value increases at a decreasing rate. In contrast, Table 3.5
illustrates the linear effects of dividends even when some of the exotic in-
puts have been changed. Whatever the change in variable is, the effects of
dividends are always very close to linear. While Table 3.5 illustrates
many options with unique dividend rates, Table 3.6 illustrates the effects
of changing dividends over time on a single option. That is, Table 3.5’s
32 IMPACTS OF THE NEW FAS 123 METHODOLOGY
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TABLE 3.3 Effects of Changing Volatilities on Option Value
Static Base Increasing Decreasing Volatility Volatility
Basic Input Parameters Year Case Volatilities Volatilities Smile Frown
Stock Price $100.00 1 55.00% 10.00% 100.00% 80.00% 35.00%
Strike Price $100.00 2 55.00% 20.00% 90.00% 70.00% 40.00%
Maturity 10.00 3 55.00% 30.00% 80.00 50.00% 50.00%
Risk-Free Rate 5.50% 4 55.00% 40.00% 70.00% 40.00% 70.00%
Dividend Rate 0.00% 5 55.00% 50.00% 60.00^ 35.00% 80.00%
Lattice Steps 10 6 55.00% 60.00% 50.00% 35.00% 80.00%
Suboptimal Behavior 1.80 7 55.00% 70.00% 40.00% 40.00% 70.00%
Vesting Period 4.00 8 55.00% 80.00% 30.00% 50.00% 50.00%

Forfeiture Rate 10.00% 9 55.00% 90.00% 20.00% 70.00% 40.00%
10 55.00% 100.00% 10.00% 80.00% 35.00%
Average 55.00% 55.00% 55.00% 55.00% 55.00%
BSM using 55% $71.48 $71.48 $71.48 $71.48 $71.48
Average Rate
Forfeiture Modified $64.34 $64.34 $64.34 $64.34 $64.34
BSM using 55%
Average Rate
Changing Volatilities $38.93 $32.35 $45.96 $39.56 $39.71
Binomial Lattice
33
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34 IMPACTS OF THE NEW FAS 123 METHODOLOGY
TABLE 3.4 Nonlinear Effects of Maturity
1.8 Behavior Multiple
1-Year Vesting
10% Forfeiture Rate
Option
Maturity Value Change
1 $25.16
2 $32.41 28.84%
3 $35.35 9.08%
4 $36.80 4.08%
5 $37.87 2.91%
6 $38.41 1.44%
7 $38.58 0.43%
TABLE 3.5 Linear Effects of Dividends
1.8 Behavior Multiple 1.8 Behavior Multiple 3.0 Behavior Multiple
4-Year Vesting 1-Year Vesting 1-Year Vesting
10% Forfeiture Rate 10% Forfeiture Rate 10% Forfeiture Rate

Dividend Option Option Option
Rate Value Change Value Change Value Change
0% $42.15 $42.41 $49.07
1% $39.94 –5.24% $41.47 –2.20% $47.67 –2.86%
2% $37.84 –5.27% $40.55 –2.22% $46.29 –2.89%
3% $35.83 –5.30% $39.65 –2.24% $44.94 –2.92%
4% $33.92 –5.33% $38.75 –2.26% $43.61 –2.95%
5% $32.10 –5.37% $37.87 –2.28% $42.31 –2.98%
$50 Stock Price
1.8 Behavior Multiple 1.8 Behavior Multiple
1-Year Vesting 1-Year Vesting
10% Forfeiture Rate 5% Forfeiture Rate
Dividend Option Option
Rate Value Change Value Change
0% $21.20 $45.46
1% $20.74 –2.20% $44.46 –2.20%
2% $20.28 –2.22% $43.47 –2.23%
3% $19.82 –2.24% $42.49 –2.25%
4% $19.37 –2.26% $41.53 –2.27%
5% $18.93 –2.28% $40.58 –2.29%
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results are based on comparing different options with different dividend
rates, whereas Table 3.6’s results are based on a single option whose under-
lying stock’s dividend yields are changing over the life of the option.
15
Clearly, a changing-dividend option has some value to add in terms of
the overall option valuation results. Therefore, if the firm’s stock pays a
dividend, then the analysis should also consider the possibility of dividend
yields changing over the life of the option.
OPTIONS WHERE BLACKOUT

PERIODS EXIST
The last item of interest is blackout periods, which can be modeled in
the binomial lattice. These are the dates on which ESOs cannot be exe-
cuted. These dates are usually several weeks before and several weeks af-
ter an earnings announcement (usually on a quarterly basis). In addition,
only senior executives with fiduciary responsibilities have these blackout
dates, and hence, their proportion is relatively small compared to the
rest of the firm. Table 3.7 illustrates the calculations of a typical ESO
with different blackout dates.
16
In the case where there are only a few
blackout days a month, there is little difference between options with
blackout dates and those without blackout dates. In fact, if the subopti-
mal behavior multiple is small (a 1.8 ratio is assumed in this case),
blackout dates at strategic times will actually prevent the option holder
Impact on Valuation 35
TABLE 3.6 Effects of Changing Dividends over Time
Option
Scenario Value Change Notes
Static 3% Dividend $39.65 0.00% Dividends are kept steady at 3%
Increasing Gradually $40.94 3.26% 1% to 5% with 1% increments
(average of 3%)
Decreasing Gradually $38.39 –3.17% 5% to 1% with –1% increments
(average of 3%)
Increasing Jumps $41.70 5.19% 0%, 0%, 5%, 5%, 5%
(average of 3%)
Decreasing Jumps $38.16 –3.74% 5%, 5%, 5%, 0%, 0%
(average of 3%)
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from exercising suboptimally and sometimes even increase the value of

the option ever so slightly.
Table 3.7’s analysis assumes only a small percentage of blackout
dates in a year (for example, during several days in a year, the ESO can-
not be executed). This may be the case for certain so-called brick-and-
mortar companies, and as such, blackout dates can be ignored.
However, in other firms such as those in the biotechnology and high-tech
industries, blackout periods play a more significant role. For instance, in
a biotech firm, blackout periods may extend 4 to 6 weeks every quarter,
straddling the release of its quarterly earnings. In addition, blackout pe-
riods prior to the release of a new product may exist. Therefore, the pro-
portion of blackout dates with respect to the life of the option may reach
upward of 35 to 65 percent per year. In such cases, blackout periods will
significantly affect the value of the option. For instance, Table 3.8 illus-
trates the differences between a customized binomial lattice with and
without blackout periods.
17
By adding in the real-life elements of black-
out periods, the ESO value is further reduced by anywhere between 10
and 35 percent depending on the rate of forfeiture and volatility. As ex-
pected, the reduction in value is nonlinear, as the effects of blackout pe-
riods will vary depending on the other input variables involved in the
analysis.
Table 3.9 shows the effects of blackouts under different dividend yields
and vesting periods, while Table 3.10 illustrates the results stemming from
different dividend yields and suboptimal exercise behavior multiples.
Clearly, it is almost impossible to predict the exact impact unless a detailed
analysis is performed, but the range can be generalized to be typically be-
tween 10 and 20 percent.
36 IMPACTS OF THE NEW FAS 123 METHODOLOGY
TABLE 3.7 Effects of Blackout Periods on Option Value

Blackout Dates Option Value
No blackouts $43.16
Every 2 years evenly spaced $43.16
First 5 years annual blackouts only $43.26
Last 5 years annual blackouts only $43.16
Every 3 months for 10 years $43.26
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Impact on Valuation 37
TABLE 3.8 Effects of Significant Blackouts (Different Forfeiture Rates and Volatilities)
% Difference
between No
Blackout Periods
versus Significant Volatility Volatility Volatility Volatility Volatility Volatility
Blackouts (25%) (30%) (35%) (40%) (45%) (50%)
Forfeiture Rate (5%) –17.33% –13.18% –10.26% –9.21% –7.11% –5.95%
Forfeiture Rate (6%) –19.85% –15.17% –11.80% –10.53% –8.20% –6.84%
Forfeiture Rate (7%) –22.20% –17.06% –13.29% –11.80% –9.25% –7.70%
Forfeiture Rate (8%) –24.40% –18.84% –14.71% –13.03% –10.27% –8.55%
Forfeiture Rate (9%) –26.44% –20.54% –16.07% –14.21% –11.26% –9.37%
Forfeiture Rate (10%) –28.34% –22.15% –17.38% –15.35% –12.22% –10.17%
Forfeiture Rate (11%) –30.12% –23.67% –18.64% –16.45% –13.15% –10.94%
Forfeiture Rate (12%) –31.78% –25.11% –19.84% –17.51% –14.05% –11.70%
Forfeiture Rate (13%) –33.32% –26.48% –21.00% –18.53% –14.93% –12.44%
Forfeiture Rate (14%) –34.77% –27.78% –22.11% –19.51% –15.78% –13.15%
TABLE 3.9 Effects of Significant Blackouts (Different Dividend Yields and
Vesting Periods)
% Difference between No
Blackout Periods versus
Significant Blackouts Vesting (1) Vesting (2) Vesting (3) Vesting (4)
Dividends (0%) –8.62% –6.93% –5.59% –4.55%

Dividends (1%) –9.04% –7.29% –5.91% –4.84%
Dividends (2%) –9.46% –7.66% –6.24% –5.13%
Dividends (3%) –9.90% –8.03% –6.56% –5.43%
Dividends (4%) –10.34% –8.41% –6.90% –5.73%
Dividends (5%) –10.80% –8.79% –7.24% –6.04%
Dividends (6%) –11.26% –9.18% –7.58% –6.35%
Dividends (7%) –11.74% –9.58% –7.93% –6.67%
Dividends (8%) –12.22% –9.99% –8.29% –6.99%
Dividends (9%) –12.71% –10.40% –8.65% –7.31%
Dividends (10%) –13.22% –10.81% –9.01% –7.64%
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TABLE 3.10 Effects of Significant Blackouts (Different Dividend Yields and Suboptimal Exercise Behaviors)
% Difference
between No
Blackout Periods
versus Significant Dividends Dividends Dividends Dividends Dividends Dividends Dividends Dividends Dividends Dividends Dividends
Blackouts (0%) (1%) (2%) (3%) (4%) (5%) (6%) (7%) (8%) (9%) (10%)
Suboptimal Behavior
Multiple (1.8) –1.01% –1.29% –1.58% –1.87% –2.16% –2.45% –2.75% –3.06% –3.36% –3.67% –3.98%
Suboptimal Behavior
Multiple (1.9) –1.01% –1.29% –1.58% –1.87% –2.16% –2.45% –2.75% –3.06% –3.36% –3.67% –3.98%
Suboptimal Behavior
Multiple (2.0) –1.87% –2.29% –2.72% –3.15% –3.59% –4.04% –4.50% –4.96% –5.42% –5.90% –6.38%
Suboptimal Behavior
Multiple (2.1) –1.87% –2.29% –2.72% –3.15% –3.59% –4.04% –4.50% –4.96% –5.42% –5.90% –6.38%
Suboptimal Behavior
Multiple (2.2) –4.71% –5.05% –5.39% –5.74% –6.10% –6.46% –6.82% –7.19% –7.57% –7.95% –8.34%
Suboptimal Behavior
Multiple (2.3) –4.71% –5.05% –5.39% –5.74% –6.10% –6.46% –6.82% –7.19% –7.57% –7.95% –8.34%
Suboptimal Behavior

Multiple (2.4) –4.71% –5.05% –5.39% –5.74% –6.10% –6.46% –6.82% –7.19% –7.57% –7.95% –8.34%
Suboptimal Behavior
Multiple (2.5) –6.34% –6.80% –7.28% –7.77% –8.26% –8.76% –9.27% –9.79% –10.32% –10.86% –11.41%
Suboptimal Behavior
Multiple (2.6) –6.34% –6.80% –7.28% –7.77% –8.26% –8.76% –9.27% –9.79% –10.32% –10.86% –11.41%
Suboptimal Behavior
Multiple (2.7) –6.34% –6.80% –7.28% –7.77% –8.26% –8.76% –9.27% –9.79% –10.32% –10.86% –11.41%
Suboptimal Behavior
Multiple (2.8) –6.34% –6.80% –7.28% –7.77% –8.26% –8.76% –9.27% –9.79% –10.32% –10.86% –11.41%
Suboptimal Behavior
Multiple (2.9) –8.62% –9.04% –9.46% –9.90% –10.34% –10.80% –11.26% –11.74% –12.22% –12.71% –13.22%
Suboptimal Behavior
Multiple (3.0) –8.62% –9.04% –9.46% –9.90% –10.34% –10.80% –11.26% –11.74% –12.22% –12.71% –13.22%
38
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SUMMARY AND KEY POINTS
■ Option valuation can be performed by applying Monte Carlo path-
dependent simulation, closed-form models (BSM, GBM, and the like),
and lattices (binomial, trinomial, multinomial, and the like).
■ Only binomial lattices can account for real-world exotic inputs such as
vesting, forfeitures, blackouts, and suboptimal exercise behavior, as well
as risk-free rates, dividends, and volatilities changing during the life of
the option. The other inputs into the binomial lattice are the same as the
GBM or simulation models (stock price, strike price, maturity, a single
risk-free rate, a single dividend yield, and a single volatility).
■ Stock price, maturity, risk-free rate, and volatility are all positively cor-
related to ESO value, whereas strike price and dividend yield are nega-
tively correlated to the ESO value.
■ Some of these exotic inputs may have a greater impact on the option
value than volatility, and if accounted for correctly may potentially re-

duce the fair-market value of the ESO.
■ These exotic inputs have nonlinear and interacting effects on option
value.
■ Vesting, suboptimal exercise behavior, and forfeitures will all reduce
the option value.
■ An increasing (decreasing) risk-free rate over time will reduce (in-
crease) an option’s value.
■ Increasing volatilities over time starting from a low level will tend to
decrease the option value slightly as compared to using an average
volatility.
■ Blackout periods tend to have significant effects on option value if they
occur frequently throughout the year.
Impact on Valuation 39
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